Aberdeen's 2-1 victory ended Fraser Forster's chances of setting a new British clean-sheet mark and scuppered the Hoops' chances of going through the entire season unbeaten.
Now the Scotland defender is looking for a reaction from his team-mates, who still have a number of records in their sights.
The lowest number of goals conceded in the top flight (18) could fall this season along with the most points (103) and fewest defeats (one), all set during the 2001-02 season.
Celtic had central defender Virgil van Dijk dismissed early in the game - a decision which infuriated manager Neil Lennon - and Mulgrew is convinced it had a major bearing on the outcome of the match.
Speaking to Celtic TV, he said: "It was disappointing to get a man sent off, that changed the game, then they scored a great goal and that you can't do anything about.
"What happened on Tuesday has played on our minds for a few days, but we need to put the result behind us and move towards the next match.
"Now we just need to focus on picking up as many points as we can. At a club like Celtic you need to bounce back. The fans want to win every game and they demand you give your all.
"The manager does as well, every day in training he is on us and it shows this season, with the unbeaten run."